An Introduction To Bridge Circuits - Why Do You Need Them?

An Introduction To Bridge Circuits - Why Do You Need Them?
        Making measurements with sensors is a common way in which many engineers and scientists encounter electrical devices.  There are many different ways in which physical variables like temperature, light intensity, pressure and numerous other physical variables can be measured electrically.  Devices used to measure a physical variable are called sensors.  Some different kinds of sensors include the following.

• Sensors which change resistance as the physical variable changes.
• Thermistors for temperature measurement
• Photo-resistors for light measurement
• Strain gages for measurement of mechanical strain
• Sensors which produce a voltage change for a change in a physical variable.
• Thermocouples for temperature
• Solar cells for light.

Other kinds of sensors might include:

• Sensors which produce some other sort of electrical change.  Some examples might include the following.
• A tachometer that produces a frequency proportional to rpm.
• Sensors which produce a set of signals in binary code proportional to pressure.
• Sensors which produce a voltage signal with a frequency proportional to flow rate.

        First, let us consider what happens if we put a temperature sensor (a thermistor) into a voltage divider circuit.  Here's the circuit.  Actually, we examined this circuit in the lesson on voltage dividers, and you should review that material if you don't remember it.  Click here for that material.


What we found in the voltage divider lesson is the following.

• At some nominal value of the temperature (if we have a temperature sensor) the voltage divider will have a nominal output voltage.
• As the temperature changes the voltage output of the voltage divider changes.
• The voltage change will probably be a nonlinear function of temperature as the temperature deviates from the nominal value of the temperature.

        There are some problems with using a voltage divider.  Consider the following.

• You might want an output signal that is zero at the nominal conditions.
• You could then have an output signal that was positive when the temperature deviated in one direction and a negative output signal when the temperature deviated in the other direction.
• If the outut is something other than temperature that becomes even more clear.
• If the sensor is a strain gage, the strain could be positive or negative, and you would want the output voltage to be similarly positive or negative, and ideally it would be proportional to strain.
• If the sensor is a pressure sensor, you could want a positive signal for a presssure above atmospheric (or any other reference) and negative for a pressure below.

The point here is that it is common to want a zero output signal under certain, known conditions.  There are several ways you could subtract out that pesky DC voltage.  For example, you could use an operational amplifier circuit to subtract out the DC voltage.  That's more complex than another solution - using a bridge circuit. Usually a bridge circuit is what is used in this situation, and in this lesson you're going to learn about bridge circuits.  Bridge circuits are simple circuits that permit us to solve the problems noted above, and you need to learn about them.

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Bridge Circuits         What is a bridge circuit?  It's easier to look at one than to try to describe it.  Here is a bridge circuit.



The bridge circuit has two arms (R_a and R_b constitute one arm here, and R_c and R_s constitute the other arm).  Each arm is composed of two resistors in series, and you may want to think of each arm as a voltage divider.  The output is the difference between the outputs of the two voltage dividers.  In the bridge circuit above we have also included some source resistance for the source which drives the bridge circuit.  This is the circuit we want to understand.

        What are you trying to do in this lesson?

• Given a sensor that changes resistance as some physical variable changes,
• Be able to use the sensor in a bridge circuit.
• Be able to choose components for the bridge circuit that will produce good performance.

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Analysis Of Bridge Circuits - Balancing The Bridge         We have noted that it might be possible to get a bridge output of zero volts.  That's true, but it only happens under certain conditions.  When the output of a bridge is zero, the bridge is said to be balanced.  The first thing we will do is to determine the conditions for a bridge circuit to be balanced.

        If the output voltage of a bridge circuit is zero, that will happen when the outputs of both dividers is the same.  Here's the bridge circuit again.  We'll probably have to be looking at it as we make this argument.

        The first thing that we notice is that both voltage dividers have the same voltage at the "top" of the bridge.  Call that voltage V_top.  Then, the voltage at the left terminal (labelled "+") is given by:



V_top. [R_b/(R_a + R_b)] Similarly, the voltage at the right terminal (labelled "-") is given by:



V_top. [R_s/(R_c + R_s)] The difference between these two voltages - the output voltage - is given by:



V_top. [R_b/(R_a + R_b)] - V_top. [R_s/(R_c + R_s)] Setting the output voltage to zero (the condition for a balanced bridge), we get:



V_top. [R_b/(R_a + R_b)] - V_top. [R_s/(R_c + R_s)] = 0 Since V_top is a common factor it can be removed.  Then, we get:



[R_b/(R_a + R_b)] - [R_s/(R_c + R_s)] = 0 or [R_b/(R_a + R_b)] = [R_s/(R_c + R_s)] Now, cross-multiply the denominators.



R_bR_c + R_bR_s= R_sR_a + R_bR_s Note that the term R_sR_b appears on both sides of the equation and can be taken out on both sides.  That gives us:



R_bR_c = R_sR_a This is the condition for balance that we were looking for.  It is a very simple relationship that must be obeyed by the resistors in the bridge portion of the circuit.